Problem: Solve for $y$, $ \dfrac{9}{10y + 6} = \dfrac{2y - 9}{15y + 9} - \dfrac{3}{5y + 3} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $10y + 6$ $15y + 9$ and $5y + 3$ The common denominator is $30y + 18$ To get $30y + 18$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{9}{10y + 6} \times \dfrac{3}{3} = \dfrac{27}{30y + 18} $ To get $30y + 18$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{2y - 9}{15y + 9} \times \dfrac{2}{2} = \dfrac{4y - 18}{30y + 18} $ To get $30y + 18$ in the denominator of the third term, multiply it by $\frac{6}{6}$ $ -\dfrac{3}{5y + 3} \times \dfrac{6}{6} = -\dfrac{18}{30y + 18} $ This give us: $ \dfrac{27}{30y + 18} = \dfrac{4y - 18}{30y + 18} - \dfrac{18}{30y + 18} $ If we multiply both sides of the equation by $30y + 18$ , we get: $ 27 = 4y - 18 - 18$ $ 27 = 4y - 36$ $ 63 = 4y $ $ y = \dfrac{63}{4}$